Critical state of non-coherent multi-state system

Abstract Non-coherent systems represent a specific group of systems in context of reliability analysis. These systems are characteristic by existence of situations in which degradation of a system component can result in improvement of the whole system. Non-coherent systems are mostly investigated in case of Binary-State Systems (BSSs) that admit two performance levels for modeling system as well as its components. Properties of these systems have been studied and algorithms for calculation of most of reliability measures have been developed. However, in case of Multi-State Systems (MSSs), the situation is completely different. Non-coherent MSSs have been studied only marginally with focus on homogeneous MSSs. In this paper, we deal with heterogeneous non-coherent MSSs, generalize existing definitions for them and develop a new approach for computation of their critical system states, which play a key role in importance analysis. The analysis of non-coherent MSSs considered in this paper is implemented based on its representation in a form of time independent structure function.